(a) An automotive engineer is investigating two different types of metering devices for an electronic fuel injection system to determine whether they differ in their fuel mileage performance. The system is installed on 10 different cars, and a test is run with each metering device on each car. The data is provided below: Metering Device Car 1 2 17.6 16.8 2 19.4 20.0 3 18.2 17 .6 4 17.1 16.4 5 15.3 16.0 6 15.9 15.9 16.3 16.5 8 18.0 18.4 9 17.3 16.4 10 19.1 20.1 (i) Is there a significant difference between the means of the two metering devices? Use a = 0.05. Interpret the result in the context of the problem. (12 marks) (b) An article in the journal Hazardous Waste and Hazardous Materials (Vol. 6, 1989) reported the results of an analysis of the weight of calcium in standard cement and cement doped with lead. Reduced levels of calcium would indicate that the hydration mechanism in the cement is blocked and would allow water to attack various locations in the cement structure. Ten samples of standard cement had an average weight percent calcium of 90.0 with a sample standard deviation of 5.0, while 16 samples of the lead-doped cement had an average weight percent calcium of 87.0 with a sample standard deviation of 4.0. It is assumed that the weight percent calcium is normally distributed. (i) Show that the variances of the two samples of cement are statistically equivalent. Use a = 0.05. (13 marks) (ii) Calculate a 95% confidence interval on the difference in means for the two types of cement. Interpret the confidence interval in the context of the question. (13 Marks)